Question

How do you multiply `(x - 1)(x + 1)(x - 3)(x + 3)`?

Answer 1

`(x-1)(x+1)(x-3)(x+3)=x^4-10x^2+9`

Explanation:

We can make the process a bit shorter by using the special product for the difference of sums:

`a^2-b^2 = (a+b)(a-b)`

Using that, we have:

`color(red)((x-1)(x+1))color(blue)((x-3)(x+3)) = color(red)((x^2-1))color(blue)((x^2-9))`

From here, we use standard methods for [multiplying binomials.](https://socratic.org/algebra/polynomials-and-factoring/multiplication-of-polynomials-by-binomials)

`(x^2-1)(x^2-9) = x^2*x^2 -9x^2-1x^2+(-1)(-9)`

`=x^4-10x^2+9`